SPDE in Hydrodynamics: Recent Progress and Prospects

SPDE in Hydrodynamics: Recent Progress and Prospects PDF

Author: Sergio Albeverio

Publisher: Springer Science & Business Media

Published: 2008-04-14

Total Pages: 183

ISBN-13: 3540784926

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Of the three lecture courses making up the CIME summer school on Fluid Dynamics at Cetraro in 2005 reflected in this volume, the first, due to Sergio Albeverio describes deterministic and stochastic models of hydrodynamics. In the second course, Franco Flandoli starts from 3D Navier-Stokes equations and ends with turbulence. Finally, Yakov Sinai, in the 3rd course, describes some rigorous mathematical results for multidimensional Navier-Stokes systems and some recent results on the one-dimensional Burgers equation with random forcing.

SPDE in Hydrodynamics: Recent Progress and Prospects

SPDE in Hydrodynamics: Recent Progress and Prospects PDF

Author: Sergio Albeverio

Publisher: Springer

Published: 2008-04-01

Total Pages: 174

ISBN-13: 3540784934

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Of the three lecture courses making up the CIME summer school on Fluid Dynamics at Cetraro in 2005 reflected in this volume, the first, due to Sergio Albeverio describes deterministic and stochastic models of hydrodynamics. In the second course, Franco Flandoli starts from 3D Navier-Stokes equations and ends with turbulence. Finally, Yakov Sinai, in the 3rd course, describes some rigorous mathematical results for multidimensional Navier-Stokes systems and some recent results on the one-dimensional Burgers equation with random forcing.

Recent Progress in the Theory of the Euler and Navier–Stokes Equations

Recent Progress in the Theory of the Euler and Navier–Stokes Equations PDF

Author: James C. Robinson

Publisher: Cambridge University Press

Published: 2016-01-21

Total Pages: 247

ISBN-13: 131658934X

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The rigorous mathematical theory of the Navier–Stokes and Euler equations has been a focus of intense activity in recent years. This volume, the product of a workshop in Venice in 2013, consolidates, surveys and further advances the study of these canonical equations. It consists of a number of reviews and a selection of more traditional research articles on topics that include classical solutions to the 2D Euler equation, modal dependency for the 3D Navier–Stokes equation, zero viscosity Boussinesq equations, global regularity and finite-time singularities, well-posedness for the diffusive Burgers equations, and probabilistic aspects of the Navier–Stokes equation. The result is an accessible summary of a wide range of active research topics written by leaders in their field, together with some exciting new results. The book serves both as a helpful overview for graduate students new to the area and as a useful resource for more established researchers.

Stochastic Geometry

Stochastic Geometry PDF

Author: W. Weil

Publisher: Springer

Published: 2006-10-26

Total Pages: 302

ISBN-13: 3540381759

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Stochastic Geometry is the mathematical discipline which studies mathematical models for random geometric structures. This book collects lectures presented at the CIME summer school in Martina Franca in September 2004. The main lecturers covered Spatial Statistics, Random Points, Integral Geometry and Random Sets. These are complemented by two additional contributions on Random Mosaics and Crystallization Processes. The book presents a comprehensive and up-to-date description of important aspects of Stochastic Geometry.

Hyperbolic Systems of Balance Laws

Hyperbolic Systems of Balance Laws PDF

Author: Alberto Bressan

Publisher: Springer

Published: 2007-05-26

Total Pages: 365

ISBN-13: 3540721878

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This volume includes four lecture courses by Bressan, Serre, Zumbrun and Williams and a Tutorial by Bressan on the Center Manifold Theorem. Bressan introduces the vanishing viscosity approach and clearly explains the building blocks of the theory. Serre focuses on existence and stability for discrete shock profiles. The lectures by Williams and Zumbrun deal with the stability of multidimensional fronts.

Random Perturbation of PDEs and Fluid Dynamic Models

Random Perturbation of PDEs and Fluid Dynamic Models PDF

Author: Franco Flandoli

Publisher: Springer

Published: 2011-03-02

Total Pages: 187

ISBN-13: 3642182313

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The book deals with the random perturbation of PDEs which lack well-posedness, mainly because of their non-uniqueness, in some cases because of blow-up. The aim is to show that noise may restore uniqueness or prevent blow-up. This is not a general or easy-to-apply rule, and the theory presented in the book is in fact a series of examples with a few unifying ideas. The role of additive and bilinear multiplicative noise is described and a variety of examples are included, from abstract parabolic evolution equations with non-Lipschitz nonlinearities to particular fluid dynamic models, like the dyadic model, linear transport equations and motion of point vortices.

Blocks and Families for Cyclotomic Hecke Algebras

Blocks and Families for Cyclotomic Hecke Algebras PDF

Author: Maria Chlouveraki

Publisher: Springer

Published: 2009-08-29

Total Pages: 173

ISBN-13: 3642030645

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This volume offers a thorough study of symmetric algebras, covering topics such as block theory, representation theory and Clifford theory. It can also serve as an introduction to the Hecke algebras of complex reflection groups.

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